In order to investigate the impact of different treatments for the contact angle (a) for heterogeneous ice nucleating properties of natural dust and black carbon (BC) particles,we implement the classical-nucleation-theory-based parameterization of heterogeneous ice nucleation (Hoose et al., 2010) in the Community Atmospheric Model version 5 (CAM5), and then improve it by replacing the originalsingle contact angle model with the probability density function of a (a-PDF) model to better represent the icenucleationbehavior of natural dust found in observations. We re-fit the classical nucleation theory (CNT) to constrain the uncertain parameters (i.e., onset a and activation energy in the single amodel; mean contact angle and standard deviation in the a-PDF model) using recent observation datasets for Saharan natural dust and BC (soot). We investigate the impact of time-dependence of droplet freezing on mixed-phase clouds and climate in CAM5, and the roles of natural dust and soot by different nucleation mechanisms. Our results show that when comparing with observations, the potential ice nuclei (IN) calculated by the a-PDF model has a better agreement than that calculated by the single-amodel at warm temperatures (T>-20oC). Ice crystals can form at lower altitudes (with warmer temperatures) simulated by the a-PDF model compared with the single-amodel in CAM5. All of these can be attributed to different ice nucleation efficiencies among aerosol particles with some particles having smaller contact angles (higher efficiencies) in the a-PDF model. In the sensitivity tests with the a-PDF model, we find that the change of mean contact angle has larger impact on the active fraction than that of standard deviation, even though the change of standard deviation can lead to the transition of freezing behavior. Both the single aand the a-PDF model indicates that the immersion freezing of natural dust plays a more important role in the heterogeneous nucleation than that of soot in mixed-phase clouds.